Cover -- Preface -- Acknowledgement -- Contents -- Unit l. Numerical Analysis-l -- Chapter 1. Calculus of Finite Differences -- 1.1 Finite Differences -- 1.2 Forward Differences -- 1.3 Backward Differences -- 1.4 Central Differences -- 1.5 Shift Operator E -- 1.6 Relations between the Operators -- 1.7 Fundamental theorem of the Difference Calculus -- 1.8 Factorial Function -- 1.9 To Show that -- 1.10 To Show that -- Solved Examples -- Exercise 1.1 -- Answers -- Chapter 2. Interpolation -- 2.1 To Find One Missing Term -- 2.2 Newton-Gregory's Formula for Forward Interpolation with Equal Intervals -- 2.3 Newton-Gregory's Formula for Backward Interpolation with Equal Intervals -- 2.4 Lagrange's Interpolation Formula for Unequal Intervals -- 2.5 Stirling's Difference Formula -- Solved Examples -- Exercise 2.1 -- Answers -- Chapter 3. Solution of Linear Simultaneous Equations -- 3.1 Linear Equations -- 3.2 Gauss Elimination Method -- 3.3 Gauss-Seidel Method -- Solved Examples -- Exercise 3.1 -- Answers -- Chapter 4. Solution of Algebraic and Transcendental Equations -- 4.1 Algebraic Equation -- 4.2 Transcendental Equation -- 4.3 Root of the Equation -- 4.4 Newton-Raphson Method -- 4.5 Regula-Falsi Method -- Solved Examples -- Exercise 4.1 -- Answers -- Chapter 5. Curve Fitting -- 5.1 Scatter Diagram -- 5.2 Curve Fitting -- 5.3 Method of Least Squares -- 5.4 Working Rule to Fit a Straight Line to Given Data by Method of Least Squares -- 5.5 Working Rule to Fit a Parabola to the Given Data by Method of Least Squares -- Solved Examples -- Exercise 5.1 -- Answers -- Unit ll Numerical Analysis-ll -- Chapter 1. Numerical Differentiation -- 1.1 Derivatives Using Forward Difference Formula -- 1.2 Derivatives Using Backward Difference Formula -- 1.3 Derivatives Using Stirling Difference Formula -- 1.4 Derivatives Using Newton's Divided Difference Formula.

Solved Examples -- Exercise 1.1 -- Chapter 2. Numerical Integration -- 2.1 A General Quadrature Formula for Equally Spaced Arguments -- 2.2 The Trapezoidal Rule -- 2.3 Simpson's One-Third Rule -- 2.4 Simpson's Three-Eighth Rule -- Solved Examples -- Exercise 2.1 -- Answers -- Chapter 3. Ordinary Differential Equations of First Order -- 3.1 Euler's Method -- 3.2 Euler's Modified Method -- 3.3 Picard's Method of Successive Approximation -- 3.4 Runge-Kutta Method -- 3.5 Milne's Series Method -- Solved Examples -- Exercise 3.1 -- Answers -- Chapter 4. Difference Equations -- 4.1 Difference Equations -- 4.2 Order of Difference Equation -- 4.3 Degree of Difference Equation -- 4.4 Solution of Difference Equation -- 4.5 Fromation of Difference Equation -- 4.6 Linear Difference Equation -- 4.7 Homogeneous Linear Difference Equation with Constant Coefficient -- 4.8 Non-Homogeneous Linear Difference Equation with Constant Coefficient -- Solved Examples -- Exercise 4.1 -- Answers -- Unit lll. Special Function -- Chapter 1. Bessel's Functions -- 1.1 Bessel's Equation -- 1.2 Solution of the Bessel's Functions -- 1.3 General Solution of Bessel's Equation -- 1.4 Integration of Bessel's Equations in Series for N=0 -- 1.5 Generating Function for Jn(X) -- 1.6 Recurrence Relation for Jn(X) -- 1.7 Orthogonal Property of Bessel's Functions -- Solved Examples -- Exercise 1.1 -- Chapter 2. Legendre's Functions -- 2.1 Introduction -- 2.2 Solution of Legendre's Equation -- 2.3 General Solution of Legendre's Equation -- 2.4 Generating Function of Legendre's Polynomial Pn(X) -- 2.5 Orthogonal Properties of Legendre's Polynomials -- 2.6 Laplace's First Integral for Pn(X) -- 2.7 Laplace's Second Integral for Pn(X) -- 2.8 Rodrigue's Formula -- 2.9 Recurrence Relations -- Solved Examples -- Exercise 2.1 -- Answer -- Unit lV. Statistics and Probability.

Chapter 1. Theory of Probability -- 1.1 Terminology and Notations -- 1.2 Definitions -- 1.3 Elementary Theorems on Probability -- 1.4 Addition Theorem of Probability -- Solved Examples -- Exercise 1.1 -- Answers -- 1.5 Independent Events -- 1.6 Conditional Probability -- 1.7 Multiplicative Theory of Probability or Theorem of Compound Probability -- Solved Examples -- Exercise 1.2 -- Answers -- 1.8 Theorem of Total Probability -- 1.9 Baye's Theorem -- Solved Examples -- Exercise 1.3 -- Answers -- 1.10 Binomial Theorem -- 1.11 Multinomial Theorem -- 1.12 Random Variable -- 1.13 Expected Value -- Solved Examples -- Exercise 1.4 -- Answers -- Chapter 2. Theoretical Distributions -- 2.1 Terminology and Notations -- 2.2 Binomial Distribution -- 2.3 Constants of Binomial Distribution -- Solved Examples -- Exercise 2.1 -- Answers -- 2.4 Poisson's Distribution -- 2.5 Constants of Poisson Distribution -- 2.6 Recurrence Formula for Poisson Distribution -- 2.7 Mode of the poisson Distribution -- Solved Examples -- Exercise 2.2 -- Answers -- 2.8 Normal Distribution -- 2.9 Constants of Normal Distribution -- 2.10 Moment About the Mean M -- 2.11 Area Under the Normal Curve -- 2.12 Properties of the Normal Distribution and Normal Curve -- Solved Examples -- Exercise 2.3 -- Answers -- Chapter 3. Correlation and Regression -- 3.1 Frequency Distribution -- 3.2 Bivariate Frequency Distribution -- 3.3 Correlation -- 3.4 Positive Correlation -- 3.5 Negative Correlation -- 3.6 Linear or Non-Linear Correlation -- 3.7 Coefficient of Correlation -- 3.8 Measurement of Correlation -- 3.9 Karl Pearson's Coefficients of Correlation -- 3.10 Probable Error -- 3.11 Correlation Coefficient for a Bivariate Frequency Distribution -- Solved Examples -- 3.12 Rank Correlation or Spearman's Coefficient of Rank Correlation -- 3.13 Rank Correlation Coefficient for Repeated Ranks.

3.14 Scatter Diagram or Dot Diagram -- Exercise 3.1 -- Answers -- 3.15 Regression -- 3.16 Line of Regression -- 3.17 Standard Error of Estimate -- Solved Examples -- Exercise 3.2 -- Answers -- Unit V. Calculus of Variations and Transforms -- Chapter 1. Calculus of Variations -- 1.1 Functional -- 1.2 Euler's Equation -- 1.3 Equivalent Forms of Euler's Equation -- 1.4 Solution of Euler's Equations -- 1.5 Strong and Weak Variations -- 1.6 Isoperimetric Problems -- 1.7 Variational Problems Involving Several Dependent Variables -- 1.8 Functionals Involving Second Order Derivatives -- Solved Examples -- Exercise 1.1 -- Answers -- Chapter 2. Z-Transform -- 2.1 Z-Transform -- 2.2 Linearity Properties -- 2.3 Change of Scale Property of Damping Rule -- 2.4 Some Standard Z-Transforms -- 2.5 Shifting Un to the Right -- 2.6 Shifting Un to the Left -- 2.7 Multiplication by n -- 2.8 Division by n -- 2.9 Initial Value Theorem -- 2.10 Final Value Theorem -- Solved Examples -- Exercise 2.1 -- Answers -- 2.11 Inverse Z-Transform -- 2.12 Convolution Theorem -- Solved Examples -- Exercise 2.2 -- Answers -- 2.13 Solution of Difference Equation by Z-Transform -- Exercise 2.3 -- Answers.